A One-Dimensional Model for Star Formation Near a "Leaky" Black Hole

In the presence of a Weyl scaling invariant cosmological action, black holes no longer have an event horizon and an apparent horizon. So they have no trapped surfaces, and may be "leaky", emitting a "black hole wind" which could lead to star formation in the neighborhood of the hole. In this paper we formulate and analyze a one-dimensional model for star formation resulting from a postulated outgoing black hole particle flux, incident on a distant spherical surface modeled as a set of planar disks surrounding the hole. Using the Toomre analysis of the Jeans instability of a disk, we compute conditions for a disk collapse instability and estimate the collapse time. We suggest a mechanism for giving the disk angular momentum around the central black hole. This gives a possible explanation for the puzzling observation of young stars forming in the vicinity of the black hole Sagittarius A* central to the Milky Way galaxy.